Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
592 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×Dic652 | C2 | semidirect |
| 2. C22×#14579688 | C2 | semidirect |
| 4. C2×#19104723 | C2 | semidirect |
| 5. #23782049 | C2 | direct (N × H) |
| 6. C2×C4×C8×C163 | C2 | semidirect |
| 10. C2×Dic652 | C22 | semidirect |
| 12. C2×#14579688 | C22 | semidirect |
| 16. #19104723 | C22 | semidirect |
| 21. C4×C8×C163 | C22 | semidirect |
| 75. C2×C163 | #495 | semidirect |
| 79. C163 | C2×#495 | semidirect |
| 86. C2×C4×C8 | D163 | semidirect |
| 101. C4×C8 | C2×D163 | semidirect |
| 156. C2 | #23782049 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic652 | 2 |
| C22×#14579688 | 2 |
| C22×D1304 | 2 |
| C2×#19104723 | 2 |
| #23782049 | 2 |
| C2×C4×C8×C163 | 2 |
| C2×#495 | 163 |